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Section 3-10 : Surface Area with Polar Coordinates

We will be looking at surface area in polar coordinates in this section. Note however that all we’re going to do is give the formulas for the surface area since most of these integrals tend to be fairly difficult.

Note that because we will pick up a \(d\theta \) from the \(ds\) we’ll need to substitute one of the parametric equations in for \(x\) or \(y\) depending on the axis of rotation. This will often mean that the integrals will be somewhat unpleasant.